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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Are the vectors (1,2) and (2,4) linearly independent?
💡 Hint: Check if one can be expressed as a multiple of the other.
Question 2
Easy
Is the set of vectors (3, 1) and (1, -4) linearly independent?
💡 Hint: Consider their direction in the 2D plane.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Two vectors are linearly independent if they are:
- A) Collinear
- B) Non-collinear
- C) Opposite
💡 Hint: Think about their direction in the plane.
Question 2
In R³, three vectors are linearly independent when they are:
- True
- False
💡 Hint: Consider the relationship of three planes.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove whether the following set of vectors: (2, 3), (4, 6), and (1, 1) is linearly independent or dependent.
💡 Hint: Use the definition of linear independence to check combinations.
Question 2
Design an example of three vectors in R³ which are linearly independent and explain why.
💡 Hint: Check their arrangement in space.
Challenge and get performance evaluation